Statistical Methods for Identifying Differentially Expressed Genes in Replicated cDNA Microarray Exp

1
Statistical Methods for Identifying
Differentially Expressed Genes in Replicated cDNA
Microarray Experiments

• Presented by Nan Lin
• 13 October 2002

2
Introduction to cDNA Microarray Experiment

• Single-slide Design
• Two mRNA samples (red/green) on the same slide
• Multiple-slide Design
• Two or more types of mRNA on different slides
• Exclude time-course experiment

3
Examples of Multiple-slide Design

• Apo AI
• Treatment group 8 mice with apo AI gene knocked
  out
• Control group 8 C57B1/6 mice
• Cy5 each of 16 mice
• Cy3 pooling cDNA from 8 control mice
• SR-BI
• Treatment group 8 SR-BI transgenic mice
• Control group 8 normal FVB mice
• Microarray Setup
• 6384 spots, 4X4 grids with 19X21 spots in each

4
Single-slide Methods

• Two types
• Based solely on intensity ratio R/G
• Take into account overall transcript abundance
  measured by RG
• Historical Review
• Fold increase/decrease cut-offs (1995-1996)
• Probabilistic modeling based on distributional
  assumptions (1997-2000)
• Consider RG (2000-2001) e.g. Gamma-Gamma-Bernoull
  i

5
Summary of Single-slide Methods

• Producing a model dependent rule drawing two
  curves in the (R,G) plane
• Power (1-Type II error rate)
• False positive rate (Type I error rate)
• Multiple testing
• Replication is needed because gene expression
  data are too noisy

6
Image Analysis

• Raw data 16-bit TIFF files
• Addressing
• Within a batch, important characteristics are
  similar
• Segmentation
• Seeded region growing algorithm
• Background adjustment
• Morphological opening (a nonlinear filter)
• Software package Spot in R environment

7
Single-slide Data Display

• Plot log2R vs. log2G
• variation less dependent on absolute magnitude
• normalization is additive for logged intensities
• evens out highly skewed distributions
• a more realistic sense of variation
• Plot Mlog2 (R/G) vs. Alog2(RG)/2
• More revealing in terms of identifying spot
  artifacts and for normalization purpose

8
Normalization

• Identify and remove sources of systematic
  variation other than differential expression
• Different labeling efficiencies and scanning
  properties for Cy3 and Cy5
• Different scanning parameters
• Print-tip, spatial or plate effects
• Red intensity is often lower than green intensity
• The imbalance between R and G varies
• across spots and between arrays
• Overall spot intensity A
• Location on the array, plate origin, etc.

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An Example Self-Self Experiment
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Normalization (Cont.)

• Global normalization
• subtract mean or median from all intensity
  log-ratios
• More complex normalization
• Robust locally weighted regression
• Mspot intensity Alocationplate origin
• Use print-tip group to represent the spot
  locations
• log2 (R/G)? log2 (R/G) l(A,j)
• l(A,j) lowess in R (0.2ltflt0.4)
• Control sequences

11
Apo AI Normalization
12
Graphical Display for Test Statistics (I)

• Test statistics
• Hj no association between treatment and the
  expression level of gene j, j1,,m.
• Two-sided alternative
• Two-sample Welch t-statistics
• Replication is essential to assess the
  variability in treatment and control group
• The joint distribution is estimated by a
  permutation procedure because the actual
  distribution is not a t-distribution

13
Graphical Display for Test Statistics (II)

• Quantile-Quantile plots

14
Graphical Display for Test Statistics (III)

• Plots vs. absolute expression levels

15
Multiple Hypothesis Testing Adjusted p-values
(I)

• P-value PjPr(TjgttjHj), j1,,m.
• Family-wise Type I Error Rate (FWER)
• The probability of at least one Type I error in
  the family
• Strong Control of the FWER
• Control the FWER for any combination of true and
  false hypotheses
• Weak Control of the FWER
• Control the FWER only under the complete null
  hypothesis that all hypotheses in the family are
  true

16
Multiple Hypothesis Testing Adjusted p-values
(II)

• Adjusted p-value for Hj
• Pjinfa Hj is rejected at FWERa
• Hj is rejected at FWER a if Pjlta
• P-value adjustment approaches
• Bonferroni
• Sidak single-step
• Holm step-down
• Westfall and Young step-down minP

17
Multiple Hypothesis Testing Estimation of
adjusted p-values (I)
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Multiple Hypothesis Testing Estimation of
adjusted p-values (II)
19
Apo AI Adjusted p-values (I)
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Apo AI Adjusted p-values (II)
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Apo AI Comparison with Single-slide Methods
22
Discussion

• M-A plots
• Normalization
• Robust local regression, e.g. lowess
• Q-Q plots Plots vs. absolute expression level
• False discovery rate (FDR)
• Replication is necessary
• Design issues
• Factorial experiments
• Joint behavior of genes
• R package SMA